Higgs Processes

This page documents Higgs production within and beyond the Standard Model
(SM and BSM for short). This includes several different processes and,
for the BSM scenarios, a large set of parameters that would only be fixed
within a more specific framework such as MSSM. Two choices can be made
irrespective of the particular model:
The partial width of a Higgs particle to a pair of gauge bosons,
W^+ W^- or Z^0 Z^0, depends cubically on the
Higgs mass. When selecting the Higgs according to a Breit-Wigner,
so that the actual mass mHat does not agree with the
nominal m_Higgs one, an ambiguity arises which of the
two to use Sey95. The default is to use a linear
dependence on mHat, i.e. a width proportional to
m_Higgs^2 * mHat, while on gives a
mHat^3 dependence. This does not affect the widths to
fermions, which only depend linearly on mHat.
This flag is used both for SM and BSM Higgses.
The partial width of a Higgs particle to a pair of gluons or photons,
or a gamma Z^0 pair, proceeds in part through quark loops,
mainly b and t. There is some ambiguity what kind
of masses to use. Default is running MSbar ones, but alternatively
fixed pole masses are allowed (as was standard in PYTHIA 6), which
typically gives a noticeably higher cross section for these channels.
(For a decay to a pair of fermions, such as top, the running mass is
used for couplings and the fixed one for phase space.)

Standard-Model Higgs, further processes

A number of further production processes has been implemented, that
are specializations of some of the above ones to the high-pT
region. The sets therefore could not be used simultaneously
without unphysical doublecounting, as further explained below.
They are not switched on by the HiggsSM:all flag, but
have to be switched on for each separate process after due consideration.

The first three processes in this section are related to the Higgs
point coupling to fermions, and so primarily are of interest for
b quarks. It is here useful to begin by reminding that
a process like b bbar -> H^0 implies that a b/bbar
is taken from each incoming hadron, leaving behind its respective
antiparticle. The initial-state showers will then add one
g -> b bbar branching on either side, so that effectively
the process becomes g g -> H0 b bbar. This would be the
same basic process as the g g -> H^0 t tbar one used for top.
The difference is that (a) no PDF's are defined for top and
(b) the shower approach would not be good enough to provide sensible
kinematics for the H^0 t tbar subsystem. By contrast, owing
to the b being much lighter than the Higgs, multiple
gluon emissions must be resummed for b, as is done by PDF's
and showers, in order to obtain a sensible description of the total
production rate, when the b quarks predominantly are produced
at small pT values.
Scattering q g -> H^0 q. This process gives first-order
corrections to the f fbar -> H^0 one above, and should only be
used to study the high-pT tail, while f fbar -> H^0
should be used for inclusive production. Only the dominant c
and b contributions are included, and generated separately
for technical reasons. Note that another first-order process would be
q qbar -> H^0 g, which is not explicitly implemented here,
but is obtained from showering off the lowest-order process. It does not
contain any b at large pT, however, so is less
interesting for many applications.
Code 911.
Scattering g g -> H^0 b bbar. This process is yet one order
higher of the b bbar -> H^0 and b g -> H^0 b chain,
where now two quarks should be required above some large pT
threshold.
Warning: unfortunately this process is rather slow, owing to a
lengthy cross-section expression and inefficient phase-space selection.
Code 912.
Scattering q qbar -> H^0 b bbar via an s-channel
gluon, so closely related to the previous one, but typically less
important owing to the smaller rate of (anti)quarks relative to
gluons.
Warning: unfortunately this process is rather slow, owing to a
lengthy cross-section expression and inefficient phase-space selection.
Code 913.

The second set of processes are predominantly first-order corrections
to the g g -> H^0 process, again dominated by the top loop.
We here only provide the kinematical expressions obtained in the
limit that the top quark goes to infinity, but scaled to the
finite-top-mass coupling in g g -> H^0. (Complete loop
expressions are available e.g. in PYTHIA 6.4 but are very lengthy.)
This provides a reasonably accurate description for "intermediate"
pT values, but fails when the pT scale approaches
the top mass.
Scattering g g -> H^0 g via loop contributions primarily
from top.
Code 914.
Scattering q g -> H^0 q via loop contributions primarily
from top. Not to be confused with the HiggsSM:bg2Hb
process above, with its direct fermion-to-Higgs coupling.
Code 915.
Scattering q qbar -> H^0 g via an s-channel gluon
and loop contributions primarily from top. Is strictly speaking a
"new" process, not directly derived from g g -> H^0, and
could therefore be included in the standard mix without doublecounting,
but is numerically negligible.
Code 916.

Beyond-the-Standard-Model Higgs, introduction

Further Higgs multiplets arise in a number of scenarios. We here
concentrate on the MSSM scenario with two Higgs doublets, but with
flexibility enough that also other two-Higgs-doublet scenarios could
be represented by a suitable choice of parameters. Conventionally the
Higgs states are labelled h^0, H^0, A^0 and H^+-.
If the scalar and pseudocalar states mix the resulting states are
labelled H_1^0, H_2^0, H_3^0. In process names and parameter
explanations both notations will be used, but for settings labels
we have adapted the shorthand hybrid notation H1 for
h^0(H_1^0), H2 for H^0(H_2^0) and
A3 for A^0(H_3^0). (Recall that the
Settings database does not distinguish upper- and lowercase
characters, so that the user has one thing less to worry about, but here
it causes probles with h^0 vs. H^0.) We leave the issue
of mass ordering between H^0 and A^0 open, and thereby
also that of H_2^0 and H_3^0.
Master switch to initialize and use the two-Higgs-doublet states.
If off, only the above SM Higgs processes can be used, with couplings
as predicted in the SM. If on, only the below BSM Higgs processes can
be used, with couplings that can be set freely, also found further down
on this page.

Beyond-the-Standard-Model Higgs, basic processes

This section provides the standard set of processes that can be
run together to provide a reasonably complete overview of possible
production channels for a single neutral Higgs state in a two-doublet
scenarios such as MSSM. The list of processes for neutral states closely
mimics the one found for the SM Higgs. Some of the processes
vanish for a pure pseudoscalar A^0, but are kept for flexiblity
in cases of mixing with the scalar h^0 and H^0 states,
or for use in the context of non-MSSM models. This should work well to
represent e.g. that a small admixture of the "wrong" parity would allow
a process such as q qbar -> A^0 Z^0, which otherwise is forbidden.
However, note that the loop integrals e.g. for g g -> h^0/H^0/A^0
are hardcoded to be for scalars for the former two particles and for a
pseudoscalar for the latter one, so absolute rates would not be
correctly represented in the case of large scalar/pseudoscalar mixing.
Common switch for the group of Higgs production beyond the Standard Model,
as listed below.

Beyond-the-Standard-Model Higgs, further processes

This section mimics the above section on "Standard-Model Higgs,
further processes", i.e. it contains higher-order corrections
to the processes already listed. The two sets therefore could not
be used simultaneously without unphysical doublecounting.
They are not controlled by any group flag, but have to be switched
on for each separate process after due consideration. We refer to
the standard-model description for a set of further comments on
the processes.

1) h^0(H_1^0) processes

Scattering q g -> h^0 q. This process gives first-order
corrections to the f fbar -> h^0 one above, and should only be
used to study the high-pT tail, while f fbar -> h^0
should be used for inclusive production. Only the dominant c
and b contributions are included, and generated separately
for technical reasons. Note that another first-order process would be
q qbar -> h^0 g, which is not explicitly implemented here,
but is obtained from showering off the lowest-order process. It does not
contain any b at large pT, however, so is less
interesting for many applications.
Code 1011.
Scattering g g -> h^0 b bbar. This process is yet one order
higher of the b bbar -> h^0 and b g -> h^0 b chain,
where now two quarks should be required above some large pT
threshold.
Warning: unfortunately this process is rather slow, owing to a
lengthy cross-section expression and inefficient phase-space selection.
Code 1012.
Scattering q qbar -> h^0 b bbar via an s-channel
gluon, so closely related to the previous one, but typically less
important owing to the smaller rate of (anti)quarks relative to
gluons.
Warning: unfortunately this process is rather slow, owing to a
lengthy cross-section expression and inefficient phase-space selection.
Code 1013.
Scattering g g -> h^0 g via loop contributions primarily
from top.
Code 1014.
Scattering q g -> h^0 q via loop contributions primarily
from top. Not to be confused with the HiggsBSM:bg2H1b
process above, with its direct fermion-to-Higgs coupling.
Code 1015.
Scattering q qbar -> h^0 g via an s-channel gluon
and loop contributions primarily from top. Is strictly speaking a
"new" process, not directly derived from g g -> h^0, and
could therefore be included in the standard mix without doublecounting,
but is numerically negligible.
Code 1016.

2) H^0(H_2^0) processes

Scattering q g -> H^0 q. This process gives first-order
corrections to the f fbar -> H^0 one above, and should only be
used to study the high-pT tail, while f fbar -> H^0
should be used for inclusive production. Only the dominant c
and b contributions are included, and generated separately
for technical reasons. Note that another first-order process would be
q qbar -> H^0 g, which is not explicitly implemented here,
but is obtained from showering off the lowest-order process. It does not
contain any b at large pT, however, so is less
interesting for many applications.
Code 1031.
Scattering g g -> H^0 b bbar. This process is yet one order
higher of the b bbar -> H^0 and b g -> H^0 b chain,
where now two quarks should be required above some large pT
threshold.
Warning: unfortunately this process is rather slow, owing to a
lengthy cross-section expression and inefficient phase-space selection.
Code 1032.
Scattering q qbar -> H^0 b bbar via an s-channel
gluon, so closely related to the previous one, but typically less
important owing to the smaller rate of (anti)quarks relative to
gluons.
Warning: unfortunately this process is rather slow, owing to a
lengthy cross-section expression and inefficient phase-space selection.
Code 1033.
Scattering g g -> H^0 g via loop contributions primarily
from top.
Code 1034.
Scattering q g -> H^0 q via loop contributions primarily
from top. Not to be confused with the HiggsBSM:bg2H1b
process above, with its direct fermion-to-Higgs coupling.
Code 1035.
Scattering q qbar -> H^0 g via an s-channel gluon
and loop contributions primarily from top. Is strictly speaking a
"new" process, not directly derived from g g -> H^0, and
could therefore be included in the standard mix without doublecounting,
but is numerically negligible.
Code 1036.

3) A^0(H_3^0) processes

Scattering q g -> A^0 q. This process gives first-order
corrections to the f fbar -> A^0 one above, and should only be
used to study the high-pT tail, while f fbar -> A^0
should be used for inclusive production. Only the dominant c
and b contributions are included, and generated separately
for technical reasons. Note that another first-order process would be
q qbar -> A^0 g, which is not explicitly implemented here,
but is obtained from showering off the lowest-order process. It does not
contain any b at large pT, however, so is less
interesting for many applications.
Code 1051.
Scattering g g -> A^0 b bbar. This process is yet one order
higher of the b bbar -> A^0 and b g -> A^0 b chain,
where now two quarks should be required above some large pT
threshold.
Warning: unfortunately this process is rather slow, owing to a
lengthy cross-section expression and inefficient phase-space selection.
Code 1052.
Scattering q qbar -> A^0 b bbar via an s-channel
gluon, so closely related to the previous one, but typically less
important owing to the smaller rate of (anti)quarks relative to
gluons.
Warning: unfortunately this process is rather slow, owing to a
lengthy cross-section expression and inefficient phase-space selection.
Code 1053.
Scattering g g -> A^0 g via loop contributions primarily
from top.
Code 1054.
Scattering q g -> A^0 q via loop contributions primarily
from top. Not to be confused with the HiggsBSM:bg2H1b
process above, with its direct fermion-to-Higgs coupling.
Code 1055.
Scattering q qbar -> A^0 g via an s-channel gluon
and loop contributions primarily from top. Is strictly speaking a
"new" process, not directly derived from g g -> A^0, and
could therefore be included in the standard mix without doublecounting,
but is numerically negligible.
Code 1056.

Parameters for Beyond-the-Standard-Model Higgs production and decay

This section offers a big flexibility to set couplings of the various
Higgs states to fermions and gauge bosons, and also to each other.
The intention is that, for scenarios like MSSM, you should use standard
input from the SUSY Les Houches
Accord, rather than having to set it all yourself. In other cases,
however, the freedom is there for you to use. Kindly note that some
of the internal calculations of partial widths from the parameters provided
do not include mixing between the scalar and pseudoscalar states.

Masses would be set in the ParticleDataTable database,
while couplings are set below. When possible, the couplings of the Higgs
states are normalized to the corresponding coupling within the SM.
When not, their values within the MSSM are indicated, from which
it should be straightforward to understand what to use instead.
The exception is some couplings that vanish also in the MSSM, where the
normalization has been defined in close analogy with nonvanishing ones.
Some parameter names are asymmetric but crossing can always be used,
i.e. the coupling for A^0 -> H^0 Z^0 obviously is also valid
for H^0 -> A^0 Z^0 and Z^0 -> H^0 A^0.
Note that couplings usually appear quadratically in matrix elements.
The h^0(H_1^0) coupling to down-type quarks.
The h^0(H_1^0) coupling to up-type quarks.
The h^0(H_1^0) coupling to (charged) leptons.
The h^0(H_1^0) coupling to Z^0.
The h^0(H_1^0) coupling to W^+-.
The h^0(H_1^0) coupling to H^+- (in loops).
Is sin(beta - alpha) + cos(2 beta) sin(beta + alpha) /
(2 cos^2theta_W) in the MSSM.
The H^0(H_2^0) coupling to down-type quarks.
The H^0(H_2^0) coupling to up-type quarks.
The H^0(H_2^0) coupling to (charged) leptons.
The H^0(H_2^0) coupling to Z^0.
The H^0(H_2^0) coupling to W^+-.
The H^0(H_2^0) coupling to H^+- (in loops).
Is cos(beta - alpha) + cos(2 beta) cos(beta + alpha) /
(2 cos^2theta_W) in the MSSM.
The H^0(H_2^0) coupling to a h^0(H_1^0) pair.
Is cos(2 alpha) cos(beta + alpha) - 2 sin(2 alpha)
sin(beta + alpha) in the MSSM.
The H^0(H_2^0) coupling to an A^0(H_3^0) pair.
Is cos(2 beta) cos(beta + alpha) in the MSSM.
The H^0(H_2^0) coupling to a h^0(H_1^0) Z^0 pair.
Vanishes in the MSSM.
The H^0(H_2^0) coupling to an A^0(H_3^0) h^0(H_1^0) pair.
Vanishes in the MSSM.
The H^0(H_2^0) coupling to a H^+- W-+ pair.
Vanishes in the MSSM.
The A^0(H_3^0) coupling to down-type quarks.
The A^0(H_3^0) coupling to up-type quarks.
The A^0(H_3^0) coupling to (charged) leptons.
The A^0(H_3^0) coupling to a h^0(H_1^0) Z^0 pair.
Is cos(beta - alpha) in the MSSM.
The A^0(H_3^0) coupling to a H^0(H_2^0) Z^0 pair.
Is sin(beta - alpha) in the MSSM.
The A^0(H_3^0) coupling to Z^0.
Vanishes in the MSSM.
The A^0(H_3^0) coupling to W^+-.
Vanishes in the MSSM.
The A^0(H_3^0) coupling to a h^0(H_1^0) pair.
Vanishes in the MSSM.
The A^0(H_3^0) coupling to H^+-.
Vanishes in the MSSM.
The A^0(H_3^0) coupling to a H^+- W-+ pair.
Vanishes in the MSSM.
The tan(beta) value, which leads to an enhancement of the
H^+- coupling to down-type fermions and suppression to
up-type ones. The same angle also appears in many other places,
but this particular parameter is only used for the charged-Higgs case.
The H^+- coupling to a h^0(H_1^0) W^+- pair.
Is cos(beta - alpha) in the MSSM.
The H^+- coupling to a H^0(H_2^0) W^+- pair.
Is 1 - cos(beta - alpha) in the MSSM.

Another set of parameters are not used in the production stage but
exclusively for the description of angular distributions in decays.
possibility to modify angular decay correlations in the decay of a
h^0(H_1) decay Z^0 Z^0 or W^+ W^- to four
fermions. Currently it does not affect the partial width of the
channels, which is only based on the above parameters.

isotropic decays.

assuming the h^0(H_1) is a pure scalar
(CP-even), as in the MSSM.

assuming the h^0(H_1) is a pure pseudoscalar
(CP-odd).

assuming the h^0(H_1) is a mixture of the two,
including the CP-violating interference term. The parameter
eta, see below, sets the strength of the CP-odd admixture,
with the interference term being proportional to eta
and the CP-odd one to eta^2.

The eta value of CP-violation in the
HiggsSM:parity = 3 option.
possibility to modify angular decay correlations in the decay of a
H^0(H_2) decay Z^0 Z^0 or W^+ W^- to four
fermions. Currently it does not affect the partial width of the
channels, which is only based on the above parameters.

isotropic decays.

assuming the H^0(H_2) is a pure scalar
(CP-even), as in the MSSM.

assuming the H^0(H_2) is a pure pseudoscalar
(CP-odd).

assuming the H^0(H_2) is a mixture of the two,
including the CP-violating interference term. The parameter
eta, see below, sets the strength of the CP-odd admixture,
with the interference term being proportional to eta
and the CP-odd one to eta^2.

The eta value of CP-violation in the
HiggsSM:parity = 3 option.
possibility to modify angular decay correlations in the decay of a
A^0(H_3) decay Z^0 Z^0 or W^+ W^- to four
fermions. Currently it does not affect the partial width of the
channels, which is only based on the above parameters.

isotropic decays.

assuming the A^0(H_3) is a pure scalar
(CP-even).

assuming the A^0(H_3) is a pure pseudoscalar
(CP-odd), as in the MSSM.

assuming the A^0(H_3) is a mixture of the two,
including the CP-violating interference term. The parameter
eta, see below, sets the strength of the CP-odd admixture,
with the interference term being proportional to eta
and the CP-odd one to eta^2.